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A group VISA algorithm for variable selection


  • Abdallah Mkhadri


  • Mohamed Ouhourane



We consider the problem of selecting grouped variables in a linear regression model based on penalized least squares. The group-Lasso and the group-Lars procedures are designed for automatically performing both the shrinkage and the selection of important groups of variables. However, since the same tuning parameter is used (as in Lasso or Lars ) for both group variable selection and shrinkage coefficients, it can lead to over shrinkage the significant groups of variables or inclusion of many irrelevant groups of predictors. This situation occurs when the true number of non-zero groups of coefficients is small relative to the number $$p$$ p of variables. We introduce a novel sparse regression method, called the Group-VISA (GVISA), which extends the VISA effect to grouped variables. It combines the idea of VISA algorithm which avoids the over shrinkage problem of regression coefficients and the idea of the GLars-type estimator which shrinks and selects the members of the group together. Hence, GVISA is able to select a sparse group model by avoiding the over shrinkage of GLars-type estimator. We distinguish two variants of the GVISA algorithm, each one is associated with each version of GLars (I and II). Moreover, we provide a path algorithm, similar to GLars, for efficiently computing the entire sample path of GVISA coefficients. We establish a theoretical property on sparsity inequality of GVISA estimator that is a non-asymptotic bound on the estimation error. A detailed simulation study in small and high dimensional settings is performed, which illustrates the advantages of the new approach in relation to several other possible methods. Finally, we apply GVISA on two real data sets. Copyright Springer-Verlag Berlin Heidelberg 2015

Suggested Citation

  • Abdallah Mkhadri & Mohamed Ouhourane, 2015. "A group VISA algorithm for variable selection," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 24(1), pages 41-60, March.
  • Handle: RePEc:spr:stmapp:v:24:y:2015:i:1:p:41-60
    DOI: 10.1007/s10260-014-0281-8

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    References listed on IDEAS

    1. Lukas Meier & Sara Van De Geer & Peter Bühlmann, 2008. "The group lasso for logistic regression," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 70(1), pages 53-71, February.
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    5. Fan J. & Li R., 2001. "Variable Selection via Nonconcave Penalized Likelihood and its Oracle Properties," Journal of the American Statistical Association, American Statistical Association, vol. 96, pages 1348-1360, December.
    6. Mkhadri, Abdallah & Ouhourane, Mohamed, 2013. "An extended variable inclusion and shrinkage algorithm for correlated variables," Computational Statistics & Data Analysis, Elsevier, vol. 57(1), pages 631-644.
    7. She, Yiyuan, 2012. "An iterative algorithm for fitting nonconvex penalized generalized linear models with grouped predictors," Computational Statistics & Data Analysis, Elsevier, vol. 56(10), pages 2976-2990.
    8. Hui Zou & Trevor Hastie, 2005. "Addendum: Regularization and variable selection via the elastic net," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 67(5), pages 768-768, November.
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